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In geometry, the **Brocard circle** (or **seven-point circle**) for a triangle is a circle defined from a given triangle. It passes through the circumcenter and symmedian of the triangle, and is centered at the midpoint of the line segment joining them (so that this segment is a diameter).

The two Brocard points lie on this circle, as do the vertices of the Brocard triangle.^{[1]} It is concentric with the first Lemoine circle.^{[2]}

If the triangle is equilateral, the circumcenter and symmedian coincide and therefore the Brocard circle reduces to a single point.^{[3]}

The Brocard circle is named for Henri Brocard,^{[4]} who presented a paper on it to the French Association for the Advancement of Science in Algiers in 1881.^{[5]}

**^**Cajori, Florian (1917),*A history of elementary mathematics: with hints on methods of teaching*, The Macmillan company, p. 261.**^**Honsberger, Ross (1995),*Episodes in Nineteenth and Twentieth Century Euclidean Geometry*, New Mathematical Library,**37**, Cambridge University Press, p. 110, ISBN 9780883856390.**^**Smart, James R. (1997),*Modern Geometries*(5th ed.), Brooks/Cole, p. 184, ISBN 0-534-35188-3**^**Guggenbuhl, Laura (1953), "Henri Brocard and the geometry of the triangle",*The Mathematical Gazette*,**37**(322): 241–243, JSTOR 3610034.**^**O'Connor, John J.; Robertson, Edmund F., "Henri Brocard",*MacTutor History of Mathematics archive*, University of St Andrews.

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